Nondegenerate curves on a Riemannian manifold

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

on a class of paracontact riemannian manifold

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

On Moduli of Nondegenerate Curves

Let Mg be the moduli space of curves of genus g ≥ 2, and let M g be the locus of curves which are birational to a curve defined by a nondegenerate bivariate Laurent polynomial. We show that dimM g = min(2g+1, 3g−3) except for g = 7 where dimM 7 = 16. In particular, a generic curve of genus g is nondegenerate if and only if g ≤ 4. Subject classification: 14M25, 14H10 Let k be a field with algebr...

Computing Geodesics on a Riemannian Manifold

Some vector fields on a riemannian manifold with semi-symmetric metric connection

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.